"The directors do not believe the connotation of the word Borough should be carried into the Football League," Wallace told the club website.
"We shall always be 'the Boro' in recognition of our roots but now its time to look to the future."
The club adopted the Borough title six months after it was reformed in 1976.
Wallace added: "Recently our supporters association asked fans to suggest a nickname for the club. That doesn't need thinking about really - the obvious choice is 'The Boro'.
"It has a place in our history so let's use it in our songs, our match programme and our conversations, just as we've done for the last 34 years."
Wallace said the change of name was decided after their Blue Square Premier title win and promotion to League Two.
"Getting out of the Blue Square Premier and into the Football League is the hardest step of all, now we have to make sure we kick on from here," he said.
"Dropping the word Borough and rebranding, by taking the name of the town is the right thing for the future."
Source: BBC Sport
Source: BBC Sport